To determine the range of the function based on the table provided, we need to identify the minimum and maximum values of [tex]\( y \)[/tex], which represent the gallons of water remaining in Raj's bathtub at different times.
Given the table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
0 & 40 \\
\hline
0.5 & 39.25 \\
\hline
1 & 38.5 \\
\hline
1.5 & 37.75 \\
\hline
\end{array}
\][/tex]
By examining the [tex]\( y \)[/tex] values:
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 40 \)[/tex]
- When [tex]\( x = 0.5 \)[/tex], [tex]\( y = 39.25 \)[/tex]
- When [tex]\( x = 1 \)[/tex], [tex]\( y = 38.5 \)[/tex]
- When [tex]\( x = 1.5 \)[/tex], [tex]\( y = 37.75 \)[/tex]
The smallest [tex]\( y \)[/tex] value in the table is 37.75 and the largest [tex]\( y \)[/tex] value in the table is 40.
Therefore, the range of the function is the set of all real numbers between these two values, inclusive of 37.75 and 40. In interval notation, this is written as [tex]\([37.75, 40]\)[/tex].
Thus, the correct answer is:
all real numbers such that [tex]\(37.75 \leq y \leq 40\)[/tex].
